Transaction networks, such as electronic wallet payment networks, grow by adding new nodes of users who can pay and be paid over the transaction network. This growth process can be slow as new users must first discover the system, realize a benefit to using the new payment system, and then create a habit of using the new payment system. Various methods have been used to try to accelerate the growth process for rewarding users based on certain desired behaviors. For example, a payment transaction network may reward an existing user a fixed monetary amount for each person they refer or by giving a certain percentage cash back or reward points for every dollar spent. These methods however typically focus on payment transactions with merchants, rather than peer-to-peer transactions, and apply rewards in a predictable manner that may not necessarily incentivize the growth behavior desired in a payment transaction network.